This invention relates to determination of stress-related reversible changes in viscoelastic materials by cyclic deformation of structures such as plastic materials, especially fibrous materials such as tire cord.
Commonly assigned U.S. Pat. No. 3,969,930 issued July 20, 1976 to D. C. Prevorsek et al. discloses an apparatus and method for testing and measuring viscoelastic solids by applying strain to the material in a substantially sinuosoidal strain wave form with resulting stress within the material as it is subjected to such strain, transforming the strain applied into an electrical strain signal having a substantially sinusoidal strain wave form, transforming the resulting stress into an electrical stress signal, having a stress wave form which may be sinusoidal or nonsinusoidal. Observations of the phase lag between the strain wave form and the stress wave form, which phase lag varies in amount and sometimes in direction depending on the characteristics of the material, permits certain conclusions to be drawn about the performance of the material in use.
We have now found that changes in viscoelastic properties as function of the stress history and the reversible changes during cyclic loading correlate with certain technologically important properties, such as creep, time to break, tendency to stress craze, etc. Hence, it is desirable to provide a method and apparatus for determining stress-related changes in viscoelastic properties, such as involving elastic modulus and mechanical loss as a function of strain.
When an elastic material is subjected to cyclic deformation under prestrain, the strain .gamma. varies according to EQU .gamma. (.theta.) = .gamma..sub.0 + .DELTA. .gamma. sin .theta.
wherein .gamma..sub.0 is the prestrain, .DELTA. .gamma. represents the strain amplitude and .theta. is the angle.
With linear viscoelastic solids the resulting stress wave is sinusoidal and shifted on the angle scale by the phase angle difference .delta., so that the stress .THETA. is represented by EQU .sigma. (.theta.) = .sigma..sub.0 + .DELTA. .sigma. sin (.theta. +.delta.)
In this case, .delta. and .DELTA. .sigma. are constant. The fraction .DELTA..sigma./.DELTA..gamma. represents the complex modulus Ex.
When the stress wave resulting from a sinusoidal strain wave is not sinusoidal, the distortion of the stress wave can result from changes in modulus as function of strain (or angle .theta.) along the cycle, or changes in mechanical loss as function of strain (or angle .theta.) during the cycle, or a combination of both, as expressed by the following equation: EQU .sigma. (.theta.) = .sigma..sub.0 + .DELTA. .sigma.(.theta.) sin [.theta. + .delta. (.theta.)]
The present invention provides a method and apparatus to determine .DELTA..sigma.(.theta.) and .delta.(.theta.).
The determination of .DELTA..sigma.(.theta.) and .delta.(.theta.) requires determination of material modulus and loss at each instant of the experiment. In accordance with the present invention this is achieved by subjecting the material to a basic, substantially sinusoidal strain wave having superimposed a cyclic strain wave of smaller amplitude and higher frequency than the basic strain wave, and extracting the desired information from the resultant composite stress wave. Thus, it is possible to carry out viscoelastic measurements which in turn reflect the material structure, while the sample is subjected to various loading histories.